Solution of triangles Questions and Answers

Exercises 9 12 12 Given Find E Right ADEF with m E EF 12V 3 DE and DE 2 m F and

Use the given information to prove that ADEF ADGF G 1 2 3 4 F D Statement EF GF 0 DF DF DE E ADEF ADGF Given EF GF DE DG Prove ADEF ADGF Reason Reason Given Reason Reason

Given the triangle below find the measure of angle A Picture is not drawn to scale A 13 20 A 24 Q degrees Give your answer accurate to at least one decimal place

9 Find EF if a DF b DF 17 and DE 15 12 and DE 8V 2 D Exercises 7 10

1 A rectangle has a width of 16 cm and a diagonal of length 20 cm How long is the rectangle

4 6 pts It is know that a triangle has A 15 a 10 b 40 Solve the triangle giving all possible solutions

The smallest side of a triangle is 5 cm and the largest side is twice the smallest side and the included angle between these sides is 65 Find the measure of the third side of the triangle 2 5 cm 7 5 cm 9 cm 12 cm

The two sides of the triangle ABC are 3 cm 5 cm and third side is 4 cm greater than the smallest side Find the measure of the smallest angle in the triangle ABC Round off to the nearest degree 180 120 38 22

A scalene triangle has sides that measure 4m 11m and 8m Find the measure of the smallest angle of this triangle 16 2 34 0 129 8 135 6

Two ships 1600 ft apart detect a submarine directly between them The angle of depression from the first ship to the submarine is 40 and from the second ship is 28 Find the distance between the first ship and the submarine 1109 ft 900 ft 1600 ft 28

D Given Find AABC APRC MZA 67 PC 5 CR 12 PR 13 AB 26 a m B b m RPC c AC d CB P A R B

9 Given Find M R Q AMNP AQRS m M 56 m R 9 QR 6 RS 7 MP 12 MN a m N b m P S P c NP d QS

B Exercises 5 6 6 a If AABC A b If AABC C to LN of AXTN T AXTN which angle of AABC corresponds N side AC of AABC AXTN which side of AXTN corresponds to

Use the power reducing formulas to rewrite sin 5x cos 5x in terms of the first power of cosine Simplify your answer as much as possible To indicate your answer first choose one of the four forms below Then fill in the blanks with the appropriate numbers OnSx cos Sx cos k cos sin 5x cos 5x coi cos O O sun 5x cos 5x cox sin 3x cos3x cos ow Transcribed Text TICKOM 2 sin u Power reducing formulas COS U S 2 tan u 1 cos2u 2 1 cos2u 2 1 cos2u 1 cos2u X 1 cos21 S

If B is an obtuse angle then in standard position it s in quadrant 2 and has the same from the previous triangle B Select C Select C Select ngle reference angle as the acute B Using the Law of Sines again gives us c for this triangle

In this example h a b so there are two triangles a triangle where B is acute 1 and a triangle where B is obtuse 2 35 b 20 C 2 We know a 15 We need to find c C and B for each triangle Acute B Triangle a b 15 sin A sin B sin 35 Solving this equation tells us that B Select 1 a 15 SO 20 sin B All of the angles of any triangle sum to 180 so C Select We can use the Law of Sines again to find c If we plug the C b values we found into sin C sin B calculate c then we can

Question Points 2 Maggie ran 3 miles east and then 4 miles north How far is she from her starting point 3 miles 4 miles O 5 miles O 7 miles

A gardener designed a circular surrounded by bushes that approximate and equilateral triangle He planted bushes at each vertex of the triangle and at 6ft intervals along its boundary Each side of the triangle is tangent to the circle which has a radius of 6 3 ft how many bushes did he use by A 6 36 60640 869 sn B 18 D 54

Solve ABC subject to the given conditions if possible Round the lengths of the sides and measures of the angles in degrees to 1 decimal place if necessary Round Intermediate steps to at least four decimal places b 833 c 21 4 109 45 O The triangle with these conditions does not exist The triangle with these conditions does exist af B 0 C 0

Find the following b if A 27 3 and c 5 kht Srove to C B a

7 Find x units 24 8 Explain the logic process you when through to arrive at your answer A What properties did you use B What formulas did you use

A D 18 Given E Exercises 17 18 Prove C B Isosceles AABE with AE BE also D and are midpoints of AE and BE respectively ABCD is an isosceles trapezoid

17 Given Prove A D E ABCD is an isosceles trapezoid AABE is isosceles C B

5 Consider any kite a Does it have line symmetry If so describe an axis of symmetry b Does it have point symmetry If so describe the point of symmetry

S X Y N T Exercises 11 14 12 If XY 6 YZ 8 and XZ 10 find a RS b ST c RT 13 If the perimeter sum of the lengths of all three sides of ARST is 20 what is the perimeter of AXYZ

6 Are the truss triangles AADB and ABFC congruent Which postulate did you use for your proof Which engineer was correct 1 point

Find the exact value of sen a if a 3 and b 5 03 34 3 3 34 34 03 34 34 O 34 3 34

Complete the statement below If z 625 cos 120 i sin 120 then any fourth root of z has r and the fourth root with least positive argument h

5 Check to see if the sides are proportional by creating ratios between corresponding sides and reducing the fractions Shortest Sides 5 Middle Sides 11 Longest Sides 13

Which of the diagrams below represents the statement If it is an equilatera triangle then it is isosceles equilateral triangle isosceles triangle Figure A O A Figure A B Figure B isosceles triangle equilateral triangle Figure B

5 In ARST M and N are the midpoints of RT and RS respectively Given MN 2x 3 ST 3x Find x MN 2 points R M S N T

8 Given AC BC and D is the midpoint of BC AB 2x 1 AC 3x 4 BD x 1 Find x AB BC X 2 points B A AB D BC C

7 The perimeter of AABC is 68 AB 2x 3 Find x AB AC AC 3x 2 and BC 4x 5 2 points B X A AB C

5 An isosceles triangle has legs of length 12 and base angles that measure 28 What is the measure of its bas to the nearest tenth Be careful on this one

3 In AQRS ZR is a right angle m Q 57 and QS 35 Which of the following expressions correctly calculates the length of QR 1 2 35 sin 57 35 cos 57 3 35 cos 57 4 35 tan 57

4 8 In the following diagram AEFG AMNP and cos E If MP 20 then find the length of MN to the 7 P nearest tenth Show the work that leads to your answer G S 20

E Using only a straightedge and a compass construct the image of AEFG after a rotation by 180 about point K shown Leave all construction marks Mark the image AE F G E K

5 Given the triangle below answer the following a Write trigonometric ratios based only on the information given for ZL and ZN ZL ratio ZN ratio b Solve both of these for the measures of ZL and ZN to the nearest tenth c What is the relationship between these two angles 10 5

3 Given right triangle DEF shown write down each of the following ratios Do not express as decimals a sin D b cos D c tan D d sin F f tan F e cos F 15 D 12 4 In any right triangle what must be true about the sum of the measures of the two acute angles Do you notice anything shout ho ging and cogine of the acute angles in 32 What do you notice

3 An isosceles triangle ABC has legs of length 24 and a vertex angle that measures 36 Determine the length of its base BC to the nearest tenth A 24 36 24

If 7 points are found on a circle how many triangles can be drawn using any 3 of these points as vertices Select one a 210 b 44 C 35 Od 38

A lighthouse is 46 m in height A boat s captain determines that the angle of elevation from his boat to the top of the lighthouse is 19 How far is the boat from the lighthouse Select one a 119 m b 145 m c 134 m d 186 m

6 In trapezoid ABCD shown below AB DC BC LDC and sides have lengths as shown a Determine the measure of ZD to the nearest degree b Find the length of AD in simplest radical form D A 7 in 5 in B 3 in C

1 point Consider the triangle below not drawn to scale b C C 11 01 ZA 16 14 ZB 33 768429 a Let a 4 b 8 and ZC 130 Find the length of side c and measure of the angles ZA and ZB in degrees Give your answer to at least 3 d places

QUESTION 17 1 POINT The polynomial f x given below f x x 3 7x 2 24x 32 Find the other has 1 as a zero zeros of f x List the zeros separated by a comma

APQR is inscribed in a circle with m P 70 m Q 80 and m R 30 What are the measures of PQ QR and PR Type integers or decimals

122 Answer Check Input answer as a b c b 50 Variables For the circle the dot represents the center 39 2 Find the value of the variables For the circle the dot represents the center I a Input answer as a b c

15 Given Find m 1 122 3 m 5 m22 m3 and m24 41 5

angles 24 and 26 have been bisected Using intuition what appears to be true of 29 formed by the bisectors 10 Make a sketch to represent two planes that are a parallel b perpendicular 11 Suppose that r is parallel to s and m 2 87 Find a mZ3 c m 1 b m 6 d m27 12 In Euclidean geometry how many lines can be drawn through a point P not on a line l that are a parallel to line e b perpendicular to line 1 2 3 X4 9 56 7 8 1 2 3 4 5 6 7 8 t S 9 Find 19 Given Find 20 In the figure BE L BE par each ot with Ex

Solve sin x 0 42 on 0 x 2 There are two solutions A and B with A B A B